”Never underestimate an exponential.”
–Carl Sagan
For reasons I can’t entirely recall now, my freshman year of high school began on Friday, September 1, 1978–the day before the Labor Day weekend, which is traditionally regarded as the last official weekend of summer. I will never forget the very first lesson of my first class–Social Studies I. It began promptly at 8:05 AM and was taught by Louie Senta. He was a gruff old man with a shock of silver hair and a gravelly voice. If I didn’t know better I would have thought he was delivered straight from central casting to play the role of an intimidating disciplinarian–a role, I might add, that he played with a persuasive amount of gusto.
After the bell rang signaling the start of class, Senta rested his steely blue eyes upon his new wide-eyed charges for what seemed like an eternity. He then posed this peculiar question: “If you had a choice between taking $100,000 a day for this entire month or accepting a single penny today and having the penny double every day for the remainder of the month, which would you select?
The class was silent, but I remember thinking, “What a stupid question.” Unbowed by the sea of incredulous, pimple-spotted faces staring back at him, Senta asked, “How many of you would choose $100,000 a day?” His face showed no emotion as he paused a moment to let us to ponder our answer.
At the time my only concern was whether the month of September had thirty or thirty-one days and, therefore, whether I would be entitled to the princely sum of $3 million or $3.1 million.
Senta called for a showing of hands. Without bothering to look around the room to seek the assurance of my peers, I shot my hand up. Only afterward did I glance around the room and note with mild satisfaction that my new classmates were just as bright as me.
To confirm what was already obvious, Senta then asked if anyone would choose the second option. No one raised their hand. Then, in a refrain that was to become all too familiar for the next four years of our lives, he ordered us, “Do the math. See how much richer you are because of your wisdom.”
Being good with numbers, I quickly doubled the penny ten times and calculated the sum to be $5.12. I continued on for another ten doublings. The figure after the twentieth iteration, I noted with a serene sense of satisfaction, was a scanty $5,242.88. Again, I pressed on in confidence. It was only after the twenty-eighth step–when the figure reached $1,342,177.28–that a sinking feeling came over me and I realized the error of my ways. After the thirtieth and final doubling I calculated I would have been entitled to $5,368,709.12–or almost $2.4 million more than if I had taken the “obvious” choice.
In retrospect I suspect that the purpose of Mr. Senta’s little exercise was twofold. For starters, the quiz was doubtlessly his way of humbling a bunch of cocky fourteen-year-old know-it-alls and demonstrating to us, in no uncertain terms, that we still had much to learn.
In a larger sense, though, I believe he was trying to teach us a more profound philosophical lesson: Things that might at first appear to be obvious are not always so. While he didn’t say it at the time, the implicit message was that it was important to understand the underlying forces that are at work in any given situation.
I tell this little story because, just as my classmates and I didn’t appreciate the power of exponential growth with regard to the penny, so many people these days also underestimate the power of exponential growth in other fields. Today there are no fewer than nine technological forces that have been and are continuing to grow at near exponential rates, and unless people begin to come to terms with the momentous changes that are afoot they are going to make some costly mistakes–mistakes that will make my hypothetical loss of $2.4 million look like child’s play.
The nine technological trends undergoing exponential advancement are computers/semiconductors, data storage, Internet bandwidth, the sequencing of the human genome, brain scanning, artificial intelligence, nanotechnology, robotics, and the advancement of knowledge itself.
Jump the Curve is not, however, a book about technology–although it will document and explore how many of these technological trends will impact the world of commerce. Rather it is a book about change andt will lay out the case for why leaders must welcome change. More importantly, it will provide a number of tangible steps that will help people and organizations embrace radical change in order to tap into the amazing possibilities that these new and profound transformations will create.
Throughout the course of this book the reader will find that I rely on a number of stories and analogies to illustrate many of the points that I am seeking to make. The reason for this is because the majority of people–especially nontechnical people for whom this book is primarily intended–do a better job of absorbing and comprehending stories and analogies than they do complex and arcane lectures about technological trends.
To this end, one of my favorite stories about the power of exponential growth is a story about the pond and the water lily. It can help anyone who needs to be jolted out of his current–or what I called a linear–mode of thinking.
In a nutshell, here’s the story: Imagine a small pond that sprouts a single lily on June 1. The lily splits into equal-sized lilies every day for a month. Further assume that the lilies of are such a size that at the end of the month the entire pond is covered with the pesky aquatic plants.
Under such a scenario what percentage of the pond do you imagine would be covered on June 20–or two-thirds of the way into this exercise? One percent? Five percent? Ten percent? Perhaps higher?
I am sorry to say that not only are all of the above guesses wrong, they are, in the words of my old teacher, Mr. Senta, “dangerously wrong.” By day twenty lilies cover roughly 0.01one one-thousandth of the pond–a wee one-tenth of 1 percent.
What transpires in the next ten days, though, is nothing short of transformational. Here”s the math (some of the numbers have been rounded slightly):
Day 20: .01%
Day 21: .02%
Day 22: .04%
Day 23: .078%
Day 24: 1.56%
Day 25: 3.125%
Day 26: 6.25%
Day 27: 12.5%
Day 28: 25%
Day 29: 50%
Day 30: 100%
I recount this story because it reveals a common misunderstanding about exponential trends. In the beginning, most people don’t even recognize the trend as exponential. For instance, a single lily growing to cover one-tenth of one percent of a pond hardly seems noteworthy, let alone deserving of special attention.
The problem with this negligence is that it can cause people to ignore or dismiss some very big and significant trends. All the while exponential math continues to weave its inextricable magic. Unfortunately, all too often, by the time people finally grasp how fast things are progressing–say on day twenty-eight of the pond example–and hope to either capitalize on its explosive growth or, alternatively, avoid being overwhelmed by its growing power, it is too late.
Here’s the point: The forces that I mentioned earlier–computers, data storage, Internet bandwidth, the sequencing of the human genome, brain scanning, artificial intelligence, genetic algorithms, robotics, nanotechnology, and knowledge–have been and are all continuing to advance at astounding rates. Yet today they cover only one-tenth of one percent of the proverbial pond.
It is essential, therefore, that the forward-thinking executive, whom I’ve chosen to call the exponential executive, think of today as being the metaphorical equivalent of day twenty in the pond analogy. The really big developments are still a few years off in the future, but they are coming fast and the time to begin preparing yourself and your organization for this is now. To survive you will need to learn how to jump the curve.
